Question

There are two black and two white balls in a box. One ball is drawn from the box without replacement. Answer the following:

(i) Find the probability of drawing second black ball when first withdrawn ball is white.

(ii) Find the probability of drawing second black ball when first withdrawn ball is black.

Answer 1

Let E₁ = Event of withdrawing first white ball

E₂ = Event of withdrawing first black ball

E₃ = Event of withdrawing second black ball.

Black and white balls are B₁, B₂, W₁ and W₂ respectively, then

E₁ = {(W₁, W₂), (W₁, B₁), (W₁, B₂), (W₂, B₁), (W₂, B₂)}

∴ n(E₁) = 5

E₂ = {(B₁, B₂), (B₁, W₁), (B₂, W₂), (B₂, W₁), (B₂, W₂)}

∴ n(E₂) = 5

E₃ = (W₁, B₁), (W₁, B₂), (W₂, B₁), (W₂, B₂)

∴ n(E₃) = 4

Again E₂ ∩ E₃ = {(W₁, B₁), (W₁, B₂) (W₂, B₁), (W₂, B₂)

∴ n(E₁ ∩ E₂)=4

Again E₂ ∩ E₃ = {(B₁, B₂)}

∴ n(E₁ ∩ E₃) = 1

(i) Probability of drawing second black ball, when first ball is white,

(ii) Probability of drawing second black ball, when first ball is black,